Salesman Problem Research Articles

Symmetric optical multipass matrix systems and the general rapid design methodology

We proposed an original type of multipass cell named symmetric optical multipass matrix system (SMMS), in which the same matrix patterns of various sizes can be formed on both sides. According to its special symmetric configurations, the SMMS design problem is modeled as a variant of the classical traveling salesman problem, which can be rapidly solved by evolutionary optimization algorithms. Two sets of 3-mirror SMMSs are designed, analyzed and built, which show superior characteristics of high stability, desirable beam quality and adjustable optical path lengths. Additionally, they can support simultaneous detection of multiple species with multi-laser channels. The proposed method is further extended to design a 4-mirror SMMS, which verifies the universality and robustness of the design methodology. The experimental observations are in consistent with the theoretical calculations. The newly proposed SMMSs have a broad application prospect in trace gas measurement.

Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations

AbstractTo optimize their order fulfillment processes, many e-commerce warehouses employ a storage assignment strategy known as scattered or mixed-shelves storage. Under this approach, unit loads of homogeneous products are divided, and individual pieces are stored in various shelves throughout the warehouse. This arrangement ensures that products that appear together on unpredictable pick lists are stored in close proximity somewhere in the huge warehouses, reducing the travel distance for pickers. Despite these advancements, efficiently guiding pickers through the warehouse remains a significant planning challenge. Since the same products can be found in multiple storage positions, the traditional picker routing problem becomes more complex, as an additional selection task arises regarding which shelf to retrieve each requested product from. While previous research has developed several tailor-made solution algorithms, we demonstrate that known transformation schemes used for different variants of the well-known Traveling Salesman Problem (TSP) can be utilized to convert the single picker routing problem with scattered storage (SPRP-SS) into a classical TSP. This approach enables us to leverage the extensive array of state-of-the-art TSP solvers. The purpose of this paper is to explore the performance of these solvers when applied to solving the SPRP-SS. Through our computational study, we found that existing TSP solvers exhibit good performance, allowing near-optimal solutions to be obtained in less than a second for real-world scale SPRP-SS instances. Moreover, the efficiency of these TSP solvers remains unaffected by the number of cross aisles in the warehouse. Consequently, we exploit this flexibility to investigate the impact of cross aisles on picking performance in scattered storage warehouses.

Bio-Inspired Optimization Algorithm Associated with Reinforcement Learning for Multi-Objective Operating Planning in Radioactive Environment.

This paper aims to solve the multi-objective operating planning problem in the radioactive environment. First, a more complicated radiation dose model is constructed, considering difficulty levels at each operating point. Based on this model, the multi-objective operating planning problem is converted to a variant traveling salesman problem (VTSP). Second, with respect to this issue, a novel combinatorial algorithm framework, namely hyper-parameter adaptive genetic algorithm (HPAGA), integrating bio-inspired optimization with reinforcement learning, is proposed, which allows for adaptive adjustment of the hyperparameters of GA so as to obtain optimal solutions efficiently. Third, comparative studies demonstrate the superior performance of the proposed HPAGA against classical evolutionary algorithms for various TSP instances. Additionally, a case study in the simulated radioactive environment implies the potential application of HPAGA in the future.

A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Intelligent optimization of inspection route based on multi-population integer coding particle swarm optimization algorithm

Aiming at the problems of premature convergence and slow convergence speed in the optimization process of single population particle swarm optimization algorithm, in order to improve the global convergence performance of particle swarm optimization algorithm, a hierarchical three-population integer coded particle swarm optimization algorithm based on grade evaluation with parallel structure is proposed and used to solve the traveling salesman problem (TSP). The algorithm imitates the form of biological aggregation in nature. In the initialization stage, three independent populations are generated according to different particle fitness, including an elite population composed of small-scale individuals with high fitness and two large-scale civilian populations composed of remaining individuals. The three populations apply the immigration strategy based on grade evaluation to exchange particles after a certain number of evolutionary generations. By applying the grade evaluation strategy, the natural law of the biological cluster is integrated into the particle swarm optimization algorithm, which effectively improves the optimization efficiency of the particle swarm optimization algorithm. The above algorithm is applied to the inspection route optimization of one of the traveling salesman problems. The results show that the improved algorithm is superior to the single population particle swarm optimization algorithm in terms of convergence speed, global optimization ability and stability.

Two-Tier Efficient QoE Optimization for Partitioning and Resource Allocation in UAV-Assisted MEC.

Unmanned aerial vehicles (UAVs) have increasingly become integral to multi-access edge computing (MEC) due to their flexibility and cost-effectiveness, especially in the B5G and 6G eras. This paper aims to enhance the quality of experience (QoE) in large-scale UAV-MEC networks by minimizing the shrinkage ratio through optimal decision-making in computation mode selection for each user device (UD), UAV flight trajectory, bandwidth allocation, and computing resource allocation at edge servers. However, the interdependencies among UAV trajectory, binary task offloading mode, and computing/network resource allocation across numerous IoT nodes pose significant challenges. To address these challenges, we formulate the shrinkage ratio minimization problem as a mixed-integer nonlinear programming (MINLP) problem and propose a two-tier optimization strategy. To reduce the scale of the optimization problem, we first design a low-complexity UAV partition coverage algorithm based on the Welzl method and determine the UAV flight trajectory by solving a traveling salesman problem (TSP). Subsequently, we develop a coordinate descent (CD)-based method and an alternating direction method of multipliers (ADMM)-based method for network bandwidth and computing resource allocation in the MEC system. Extensive simulations demonstrate that the CD-based method is simple to implement and highly efficient in large-scale UAV-MEC networks, reducing the time complexity by three orders of magnitude compared to convex optimization methods. Meanwhile, the ADMM-based joint optimization method achieves approximately an 8% reduction in shrinkage ratio optimization compared to baseline methods.

Improvement to application of PSO algorithm on TSP problems

In the field of swarm intelligence algorithms, particle swarm optimization algorithms have the ability of fast search and are widely used in lots of application scenarios because they are easy to implement. Therefore, different improvements have been made for their various properties. In this paper, aiming to accelerate its convergence speed, we further improve the existing hybrid particle swarm algorithm by using the idea of self adaptive and simulated annealing, examining its performance by solving Travelling salesman problem. It demonstrate that the relevant improvements can optimize the algorithm performance and have better convergence speed when iteration value was set 30, 50, or 70 by making comparions between the experiment results of both algorithm. The code used in this article is available on github. The experimental results show that the optimization proposed in this paper can optimize the algorithm to a certain extent at 30, 50, and 70 iterations, mainly because the improved algorithm can keep the convergence speed stable in more iterations.

A two-stage budget-feasible mechanism for mobile crowdsensing based on maximum user revenue routing

Through user participation, mobile crowdsensing (MCS) services overcome the problem of the excessive costs of relying solely on the active deployment of sensors and of achieving large-scale and low-cost applications of the Internet of Things, which is a research hotspot. However, current research on MCS issues adopts the perspective of service providers and does not consider user strategies, so the corresponding models cannot accurately reflect the complete status of the system. Therefore, this paper decomposes the MCS problem into a two-stage game process. By doing so, the strategies of both users and service providers can be considered, thus maximizing the interest for both parties. In the first stage, users determine the optimal route based on information released by the service provider. In the second stage, the service provider determines the winning users and the corresponding payment plan based on the route and bid information submitted by all users. Specifically, we express the user’s optimal route decision-making problem as a traveling salesman problem with time windows and node number constraints. Accordingly, we design the F-MAX-RR algorithm based on an evolutionary algorithm. We show that this algorithm can achieve an approximation ratio of (1−1/e), with the expected number of iterations being 8eL2(L+1)M. In the second stage, to maximize the total utility of the system, we transform the problem into an integer programming model with a budget constraint, which satisfies submodular characteristics. We design the S-MAX-TUM mechanism based on monotonic allocation and critical price theory to solve the problem of winning user decision-making and pricing. We demonstrate the economic characteristics of the mechanism, including truthfulness, individual rationality, and budget feasibility. The experimental results indicate the effective performance of the designed mechanisms.

Hamiltonian Cycles on Ammann-Beenker Tilings

We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings. Using this result, and the discrete scale symmetry of AB tilings, we find exact solutions to a range of other problems which lie in the complexity class NP-complete for general graphs. These include the equal-weight traveling salesperson problem, providing, for example, the most efficient route a scanning tunneling microscope tip could take to image the atoms of physical quasicrystals with AB symmetries; the longest path problem, whose solution demonstrates that collections of flexible molecules of any length can adsorb onto AB quasicrystal surfaces at density one, with possible applications to catalysis; and the three-coloring problem, giving ground states for the q-state Potts model (q≥3) of magnetic interactions defined on the planar dual to AB, which may provide useful models for protein folding. Published by the American Physical Society 2024

Enhancing the multiple traveling salesman problem solutions through Harris Hawks optimization and machine learning techniques

Enhancing the multiple traveling salesman problem solutions through Harris Hawks optimization and machine learning techniques

A faster heuristic for the traveling salesman problem with drone

A faster heuristic for the traveling salesman problem with drone

Secure Travel Planning Using a Heuristic Algorithm

Security perception in the urban area has a significant effect on travel behaviour, preferences, and tour planning. The perceptions of security risks can vary depending on factors, such as age, gender, and previous experiences. This study aims to consider security risks when developing travel plans and schedules for various activities. An improved heuristic algorithm, based on the Travelling Salesman Problem with security parameter and flexibility aspects, is proposed. Public transport is considered in three situations: fixed, flexible, and flexible-security situations. The outcomes demonstrate that the flexible situation significantly decreases travel times by 21% compared to the basic (fixed) situation. At the same time, with a slightly increased travel time the security risk can be avoided in the flexible-security situation. Travelers can enjoy a higher quality of travelling and enhanced personal experience by minimizing the journey duration and the impact of security risks on the tour schedule. The proposed method provides significant benefits for transport operators by increasing the efficiency of the transportation system and higher customer satisfaction.

Exploring the Potential of DNA Computing for Complex Big Data Problems: A Case Study on the Traveling Car Renter Problem.

The traveling car renter problem (TCRP) is a variant of the Traveling Salesman Problem (TSP) wherein the salesman utilizes rented cars for travel. The primary objective of this problem is to identify a solution that minimizes the cumulative operating costs. Given its classification as a non-deterministic polynomial (NP) problem, traditional computers are not proficient in effectively resolving it. Conversely, DNA computing exhibits unparalleled advantages when confronted with NP-hard problems. This paper presents a DNA algorithm, based on the Adleman-Lipton model, as a proposed approach to address TCRP. The solution for TCRP can be acquired by following a series of fundamental steps, including coding, interaction, and extraction. The time computing complexity of the proposed DNA algorithm is O(n2m) for TCRP with n cities and m types of cars. By conducting simulation experiments, the solutions for certain instances of TCRP are computed and compared to those obtained by alternative algorithms. The proposed algorithm further illustrates the potential of DNA computing, as a form of parallel computing, to address more intricate large-scale problems.

Comparative Study of Reduced Parameter Versions of the Bees Algorithm for Traveling Salesman Problem

Metaheuristics have shown dominance over exact methods with their capability to find near-optimal solutions to complex problems in a shorter time. Among these metaheuristics, the Bees Algorithm (BA) has proven its performance in various applications. However, fine-tuning the parameters of the BA is challenging due to its numerous parameters. There have been few studies aiming to reduce the number of parameters while maintaining or improving performance, such as the ternary BA, two-parameter BA, and Fibonacci BA. This paper reviews these variants for combinatorial problems using 13 datasets from the Travelling Salesman Problem TSPLIB. The results were compared using an independent t-test in conjunction with descriptive statistics. The findings show that the Fibonacci BA outperforms other variants, and potential suggestions for improvements in the future were proposed.

Geometric reasoning on the euclidean traveling salesperson problem in answer set programming1

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. Many instances and real world applications fall into the Euclidean TSP special case, in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. It is worth noting that in the Euclidean TSP more information is available than in the general case; in a previous publication, the use of geometric information has been exploited to speedup TSP solving for Constraint Logic Programming (CLP) solvers. In this work, we study the applicability of geometric reasoning to the Euclidean TSP in the context of an ASP computation. We compare experimentally a classical ASP approach to the TSP and the effect of the reasoning based on geometric properties. We also compare the speedup of the additional filtering based on geometric information on an ASP solver and a CLP on Finite Domain (CLP(FD)) solver.

Special Issue: Selected papers from the AIxIA 2023 Workshops

The 2023 edition of the AIxIA Conference, held in Rome, brought together a large number of researchers and practitioners to discuss the most recent and important advancements in Artificial Intelligence (AI). The conference featured 19 workshops, organized by 77 experts, attracting 248 submissions and resulting in 16 proceedings. This special issue presents extended versions of selected papers initially showcased at these workshops. Each paper underwent rigorous review and represents a diverse array of topics, reflecting the multifaceted nature of the Italian AI community. The topics covered include ethical foundations to symbiotic AI, symbolic knowledge extraction from black-box models, creative influence prediction using graph theory, AI approaches to multidimensional poverty prediction, an assessment of AI-based supports for informal caregivers, deep learning-based EEG denoising, AI-assisted board-game-based learning, large language models for assessment and feedback in higher education, geometric reasoning in the Traveling Salesperson Problem, defeasible reasoning in weighted knowledge bases, and conditional computation in neural networks. These contributions demonstrate the innovative and interdisciplinary research within the AI community, offering valuable insights and advancing the field.

ОПТИМИЗАЦИЯ ПОСЛЕДОВАТЕЛЬНОСТИ ВЫПОЛНЕНИЯ ЗАКАЗОВ ПРЕДПРИЯТИЯ ЭВРИСТИЧЕСКИМИ АЛГОРИТМАМИ

The production process of fulfilling orders with parameters that require equipment readjustment is considered. The problem of determining the optimal strategy for the production equipment changeover is an optimization problem, which is formulated as a travelling salesman problem. When solving such a task, the graph nodes are orders, the arcs are changeovers with a known cost when moving from one order to another. The optimization criterion is the minimum total cost of equipment changeovers. Based on the cost matrix of equipment changeovers when executing orders with the known parameters, research is carried out to solve the problem using the 2-opt local search algorithm and the genetic algorithm. Examples are given for estimating the total cost of changeovers for orders that have several parameters with different levels. The steps for implementing heuristic algorithms to solve the problem are presented, and the results of experiments are shown.

Integrating Inventory Management and Distribution: A Holistic Supply Chain Strategy

This study/research delves into an integrated approach to inventory management, shedding light on various inventory management technologies applicable across different industries and distribution systems. The overarching goal is to attain a competitive edge by reducing costs and enhancing service quality. It underscores the significant impact of total logistics costs, encompassing transportation, facility, and inventory expenses, on a company's competitiveness. By harmonizing inventory and distribution policy decisions, businesses can streamline costs and enhance their ability to respond effectively to market demands. The effectiveness of this integration is illustrated through a practical example involving a scenario of single supply and multiple demands. Moreover, the study examines the pivotal role of Vendor Managed Inventory in optimizing inventory management throughout the supply chain. Additionally, it explores the utilization of the Traveling Salesman Problem to streamline transportation expenses. Through the adoption of this integrated approach, organizations can realize cost efficiencies and bolster their responsiveness, ultimately strengthening their competitive position within the industry.

An ALNS metaheuristic for the family multiple traveling salesman problem

This paper presents a novel variant of the Family Traveling Salesman Problem (FTSP), a well-known NP-hard problem introduced by Morán-Mirabal et al. (2014). In the FTSP, the set of nodes is partitioned into several subsets called families, and the aim is to determine the minimum-cost cycle that begins and ends at the depot and visits a predefined number of nodes in each family. We extend the FTSP by requiring that m tours be generated, each having a number of nodes between a minimum and a maximum quantity, thus yielding the family multiple traveling salesman problem (FmTSP). We present a two-index MIP formulation and develop an ALNS metaheuristic as a solution method for large-sized instances. Our proposed ALNS was initially employed to solve the FTSP benchmark instances and allowed us to improve some of the best-known solutions. The results for new derived instances requiring multiple tours show that our ALNS also achieves optimality for all instances with proven-optimal solutions.

Solving pick-up and delivery problems via deep reinforcement learning based symmetric neural optimization

Recently, there has been a growing trend to use deep reinforcement learning (DRL) to solve NP-hard combinatorial optimization problems such as routing problem, where a policy learned by a deep neural network guides the sequential construction of solutions. Despite their success, most of the previous studies omit the symmetry between the partitions of instances and between solutions, which makes them less effective in handling the more practical scenarios with symmetric features, such as pick-up and delivery problems (PDPs). PDPs are more challenging and practical than traditional routing problems because the correlation between pick-up nodes and delivery nodes in the former is multiple one-to-one and not simple as the correlation in the latter. Besides, most DRL-based methods cannot take both computational cost and the quality of solutions into account. To resolve this issue, we propose the Symmetric Neural Optimization for Pick-up and Delivery Problems (PD-SNO) to solve the pick-up and delivery traveling salesman problem (PDTSP) and the multi-commodity one-to-one pick-up and delivery traveling salesman problem (m-PDTSP), respectively. The PD-SNO leverages the symmetries between different partitions of instances to effectively capture the relationship between symmetric node sets (i.e., pick-up nodes and delivery nodes); the PD-SNO also leverages the symmetry between different trajectories of solution to guide the construction of solutions and training of policy. We evaluate the performance of our PD-SNO, and the results show that it outperforms various representative baselines, including traditional methods (both exact and heuristic algorithms) and state-of-the-art DRL-based methods (both construction and improvement types) on synthetic datasets. Then, we further assess the generalization performance of our PD-SNO on benchmark datasets. Finally, we research the independent effectiveness of our designs through ablation studies.